Let \(w^\pi = (w^\pi _1, \ldots ,w^\pi _n)\)  denote the wait times of these teleportation requests. Because requests can be removed from the buffer without service, we will assign wait times of infinity to those requests.
Our proof that \(\gamma \)  is optimal is based on showing \(w^\pi \prec ^ww^\gamma \) , \(\pi \in \Pi \) .
Note that the standard definition [1]} corresponds to the case \(m=0\) . We introduce an operator \(T_{ij}\) , called the "\(T\) -transform", as follows. Let \(x\in \mathbb {R}_+^n\) ;
\(T_{ij} = \lambda I + (1-\lambda )Q_{ij}\) 
